What is a quantity implicature?

If the speaker is assumed to be observing the maxim, then the addressee makes a standard implicature. If the speaker is assumed to be flouting the maxim, then the addressee makes a more non-standard type of implicature.

Examples (English)

The utterance Nigel has 14 children commonly implicates ‘Nigel has only 14 children’, even though it would be compatible with Nigel’s having 20 children.